problem 2.1

Viscous friction

Suppose that a Poiseuille flow of a Newtonian viscous fluid (with shear viscosity ?) is maintained in a channel between two parallel walls under a pressure gradient in x direction, where the walls are located at y = 0 and y = d in the ( x, y) plane [Fig. 2.6(a)]. The fluid velocity is represented by the form ( u( y) , 0), where

with the maximum velocity U (see Sec. 4.6.1) at the center line y = d/2. Determine the viscous friction force F per unit distance along the channel.

Figure 2.6: (a) Velocity distribution u(y); (b) Temperature distribution T(z).

problem 2.2

Steady thermal conduction

Suppose that a horizontal fluid layer of thickness d is at rest between two horizontal walls and that the temperatures of the lower and upper walls are maintained at T ₁ and T ₂, respectively, where T ₂ > T ₁, and that the z axis is taken in the vertical direction with the lower wall at z = 0 [Fig. 2.6(b)]. Find the equation governing the steady temperature distribution T( z), and determine the temperature T( z) by solving the equation, which is given as

(The problem of steady thermal conduction will be considered in Sec. 9.4.2 again.)

problem 2.3

Initial value problem of diffusion equation

An initial value problem...